cross validation
Required packages
Variables used:
Prepare the dataset for modeling， removed stations with more than 25% of missing values
## [1] "radiation" "nightlight_450" "nightlight_4950"
## [4] "nightlight_3150" "nightlight_900" "elevation"
## [7] "industry_1000" "industry_100" "industry_3000"
## [10] "industry_300" "industry_5000" "industry_500"
## [13] "population_1000" "population_3000" "population_5000"
## [16] "road_class_1_1000" "road_class_1_100" "road_class_1_3000"
## [19] "road_class_1_300" "road_class_1_5000" "road_class_1_500"
## [22] "road_class_2_1000" "road_class_2_100" "road_class_2_3000"
## [25] "road_class_2_300" "road_class_2_5000" "road_class_2_500"
## [28] "road_class_3_1000" "road_class_3_100" "road_class_3_3000"
## [31] "road_class_3_300" "road_class_3_5000" "road_class_3_500"
## [34] "temperature_2m_10" "temperature_2m_11" "temperature_2m_12"
## [37] "temperature_2m_1" "temperature_2m_2" "temperature_2m_3"
## [40] "temperature_2m_4" "temperature_2m_5" "temperature_2m_6"
## [43] "temperature_2m_7" "temperature_2m_8" "temperature_2m_9"
## [46] "trop_mean_filt" "wind_speed_10m_10" "wind_speed_10m_11"
## [49] "wind_speed_10m_12" "wind_speed_10m_1" "wind_speed_10m_2"
## [52] "wind_speed_10m_3" "wind_speed_10m_4" "wind_speed_10m_5"
## [55] "wind_speed_10m_6" "wind_speed_10m_7" "wind_speed_10m_8"
## [58] "wind_speed_10m_9" "mean_value"Data summary
Use H2o for kfold CV and get predictions. Initialize h2o, requires Java and JDK to be installed.
Add predictions to the csv file
sf object of data, for visualization and spatial cross-validation
Variable importance of Lasso
Variable importance of ML methods: 20-times bootstrapping
Bootstrapped cross-validation
XGBRF
XGB-G
## Connection successful!
##
## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
## R Version: R version 4.1.1 (2021-08-10)
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
## R Version: R version 4.1.1 (2021-08-10)
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## R is connected to the H2O cluster:
## H2O cluster uptime: 2 days 6 hours
## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
## R Version: R version 4.1.1 (2021-08-10)
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## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## H2O cluster timezone: Europe/Amsterdam
## H2O data parsing timezone: UTC
## H2O cluster version: 3.36.0.2
## H2O cluster version age: 8 days
## H2O cluster name: H2O_started_from_R_meng_kpb162
## H2O cluster total nodes: 1
## H2O cluster total memory: 1.44 GB
## H2O cluster total cores: 8
## H2O cluster allowed cores: 8
## H2O cluster healthy: TRUE
## H2O Connection ip: localhost
## H2O Connection port: 54321
## H2O Connection proxy: NA
## H2O Internal Security: FALSE
## H2O API Extensions: Amazon S3, XGBoost, Algos, Infogram, AutoML, Core V3, TargetEncoder, Core V4
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## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Thu, Feb 03, 2022 - 17:21:42
## \begin{table}[!htbp] \centering
## \caption{}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} cccccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & LA & RF & XGB & XGB\_GAMMA & RF\_Lasso \\
## \hline \\[-1.8ex]
## RMSE & $7.57$ & $7.57$ & $7.42$ & $8.89$ & $7.34$ \\
## RRMSE & $0.32$ & $0.32$ & $0.31$ & $0.38$ & $0.31$ \\
## IQR & $8.46$ & $7.42$ & $6.86$ & $9.04$ & $7.42$ \\
## rIQR & $0.39$ & $0.34$ & $0.32$ & $0.42$ & $0.34$ \\
## MAE & $5.74$ & $5.57$ & $5.19$ & $6.23$ & $5.38$ \\
## rMAE & $0.24$ & $0.24$ & $0.22$ & $0.26$ & $0.23$ \\
## rsq & $0.64$ & $0.64$ & $0.65$ & $0.50$ & $0.66$ \\
## explained\_var & $0.64$ & $0.64$ & $0.65$ & $0.53$ & $0.66$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}Spatial cross-validation
Sp1 is purely spatial, sp2 and sp3 more specific for air quality, based on the local environment of ground stations. sp2 is easily applicable to the grid.
- sp1: spatial blocked cv (see R script “SPblock_repr”). - sp2: based on customized predictors (e.g. road_class_2_25>0 && population >1000
SP2 customized
- “tr_hp”: close to roads, high population
- “tr_mlp”: close to roads, middle-low population
- “f”: far away from roads
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## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Thu, Feb 03, 2022 - 17:23:24
## \begin{table}[!htbp] \centering
## \caption{}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} ccccccccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & RMSE & RRMSE & IQR & rIQR & MAE & rMAE & rsq & explained\_var \\
## \hline \\[-1.8ex]
## LA\_tr\_hp & $12.46$ & $0.32$ & $16.60$ & $0.43$ & $10.13$ & $0.26$ & $0.14$ & $0.21$ \\
## RF\_tr\_hp & $11.84$ & $0.30$ & $16.47$ & $0.43$ & $9.64$ & $0.25$ & $0.22$ & $0.27$ \\
## XGB\_tr\_hp & $14.29$ & $0.37$ & $15.89$ & $0.41$ & $11.03$ & $0.28$ & $$-$0.13$ & $0.23$ \\
## LA\_tr\_lmp & $7.12$ & $0.31$ & $9.68$ & $0.47$ & $5.74$ & $0.25$ & $0.19$ & $0.19$ \\
## RF\_tr\_lmp & $7.64$ & $0.34$ & $9.99$ & $0.48$ & $5.97$ & $0.26$ & $0.07$ & $0.14$ \\
## XGB\_tr\_lmp & $9.47$ & $0.42$ & $9.65$ & $0.47$ & $7.20$ & $0.32$ & $$-$0.44$ & $0.11$ \\
## LA\_far & $4.75$ & $0.35$ & $4.66$ & $0.38$ & $3.99$ & $0.30$ & $0.47$ & $0.66$ \\
## RF\_far & $4.39$ & $0.32$ & $4.11$ & $0.33$ & $3.27$ & $0.24$ & $0.55$ & $0.67$ \\
## XGB\_far & $3.51$ & $0.26$ & $4.04$ & $0.32$ & $2.62$ & $0.19$ & $0.71$ & $0.74$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}##
## % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Thu, Feb 03, 2022 - 17:23:24
## \begin{table}[!htbp] \centering
## \caption{}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} ccccccccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & RMSE & RRMSE & IQR & rIQR & MAE & rMAE & rsq & explained\_var \\
## \hline \\[-1.8ex]
## LA\_tr\_hp & $12.5$ & $0.3$ & $16.6$ & $0.4$ & $10.1$ & $0.3$ & $0.1$ & $0.2$ \\
## RF\_tr\_hp & $11.8$ & $0.3$ & $16.5$ & $0.4$ & $9.6$ & $0.2$ & $0.2$ & $0.3$ \\
## XGB\_tr\_hp & $14.3$ & $0.4$ & $15.9$ & $0.4$ & $11.0$ & $0.3$ & $$-$0.1$ & $0.2$ \\
## LA\_tr\_lmp & $7.1$ & $0.3$ & $9.7$ & $0.5$ & $5.7$ & $0.3$ & $0.2$ & $0.2$ \\
## RF\_tr\_lmp & $7.6$ & $0.3$ & $10.0$ & $0.5$ & $6.0$ & $0.3$ & $0.1$ & $0.1$ \\
## XGB\_tr\_lmp & $9.5$ & $0.4$ & $9.7$ & $0.5$ & $7.2$ & $0.3$ & $$-$0.4$ & $0.1$ \\
## LA\_far & $4.8$ & $0.4$ & $4.7$ & $0.4$ & $4.0$ & $0.3$ & $0.5$ & $0.7$ \\
## RF\_far & $4.4$ & $0.3$ & $4.1$ & $0.3$ & $3.3$ & $0.2$ & $0.5$ & $0.7$ \\
## XGB\_far & $3.5$ & $0.3$ & $4.0$ & $0.3$ & $2.6$ & $0.2$ & $0.7$ & $0.7$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}